Slow Spin Dynamics and Self-Sustained Clusters in Sparsely Connected Systems

Abstract

To identify emerging microscopic structures in low temperature spin glasses, we study self-sustained clusters (SSC) in spin models defined on sparse random graphs. A message-passing algorithm is developed to determine the probability of individual spins to belong to SSC. Results for specific instances, which compare the predicted SSC associations with the dynamical properties of spins obtained from numerical simulations, show that SSC association identifies individual slow-evolving spins. This insight gives rise to a powerful approach for predicting individual spin dynamics from a single snapshot of an equilibrium spin configuration, namely from limited static information, which can be used to devise generic prediction tools applicable to a wide range of areas.

References in corpus (15)

• The Bethe lattice spin glass revisited
• Gibbs States and the Set of Solutions of Random Constraint Satisfaction Problems
• Identifying structural flow defects in disordered solids using machine learning methods
• Replica Symmetry Breaking in Short-Range Spin Glasses: Theoretical Foundations and Numerical Evidences
• Clusters of solutions and replica symmetry breaking in random k-satisfiability
• On the freezing of variables in random constraint satisfaction problems
• Glassy dynamics near zero temperature
• Time scale separation and heterogeneous off-equilibrium dynamics in spin models over random graphs
• The large deviations of the whitening process in random constraint satisfaction problems
• Signature of the Ground-State Topology in the Low-Temperature Dynamics of Spin Glasses
• Message passing and Monte Carlo algorithms: connecting fixed points with metastable states
• Domain growth within the backbone of the three-dimensional $\pm J$ Edwards-Anderson spin glass
• Minimizing Unsatisfaction in Colourful Neighbourhoods
• Self-sustained Clusters and Ergodicity Breaking in Spin Models
• Self-Sustained Clusters as Drivers of Computational Hardness in $p$-spin Models

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